Here is the 3rd assignment for Fundamentals of Astronomical
Imaging, Winter quarter 2006-07. The writeup is due Friday, Jan 12.

FYI, I'll be out of town Jan 8-10 -- at the American
Astronomical Society semin-annual meeting, in Seattle -- so
there will be no 'formal' class Monday or Weds of the week
after break. Though naturally that shouldn't stop you from
coming in at the usual time and completing the assignment below!
(I expect to be able to check email Monday and Tuesday, Jan 8-9, so
send questions if any arise.)

Enjoy!

-Joel

***

Part I: collect background info on 2MASS and Spitzer

1) As we discussed Wednesday, do a little research on the
   "twin" (north and south) Two Micron All-Sky Survey
   (2MASS) imaging system and the Spitzer Space
   Telescope. Things to hunt down:

   a) what is the aperture (diameter) of the primary mirror
   for each telescope?

   b) what types of detectors are used, over what wavelength
   ranges can they detect infrared radiation, and what is their
   'format' (that is, how many pixels do they have along the
   X and Y directions)? (For Spitzer, pay attention only to the IRAC
   (near- to mid-infrared) and MIPS (mid- to far-infrared)
   camera systems -- don't worry about the InfraRed
   Spectrograph [IRS].)

   c) what are the typical (or allowed) exposure times for
   images obtained with 2MASS and Spitzer?

   Be sure to cite your source(s) for this info -- wikipedia
   not allowed! The first places I'd suggest to go would be the
   'official' project/mission websites
   http://www.ipac.caltech.edu/2mass/ 
   and
   http://www.spitzer.caltech.edu/.

Part II: measure 2MASS image PSF widths and compare w/
expected PSF widths

2) Read the 2MASS J-band image into ds9. Zoom way in on V1647
   Ori. Activate the 'vertical cut graph' (under either the
   'view' or 'analysis' menu, depending on which version of
   ds9 you're using) and the 'pixel table' (under
   'analysis'). Using these tools, determine the so-called
   "full width at half maximum" (FWHM) of V1647 Ori in the J-band
   image. That is, measure the number of pixels it takes to go
   from 1/2 of the maximum value on one side of (south of) V1647 Ori to
   1/2 of the maximum value on the other (north) side.

3) Measure the (angular) width of a pixel in the J-band
   image in arcseconds, using 2 methods:
   a) run the cursor from the bottom to the top of a single pixel,
   and note the change in the declination reading (in
   arcseconds) at the top of ds9;
   b) display the FITS image header (under the 'file' menu)
   and note the value of CDELT1 ('Axis 1 Pixel Size') -- which
   will most likely be in degrees. Convert this value to
   arcsec (recall: 1 degree = 3600 arcsec).

4) Multiply the result of (2), i.e. number of pixels decribing
   the FWHM of the V1647 Ori image, by the result of (3),
   i.e. arcsec per pixel.

   Congratulations, you have just measured the width of the Point Spread
   Function (PSF) of the J-band image! (The FWHM of the PSF in
   arcsec is the usual way to describe this fundamental
   characteristic of any astronomical imaging system.)

5) Repeat for the H and K images. How do the results change as
   wavelength increases? 

6) Now compare your results for the measured PSF width of
   the 2MASS images with the theoretically predicted value,
   theta = 1.2 * lambda/D,
   where:
   theta = theoretical FWHM of PSF in **radians**
   lambda = wavelength of observation
   D = telescope aperture (diameter of primary mirror)

   Does observation match theory? If not, why not?

   [NOTE: the above equation will yield the PSF FWHM in
   **radians** -- recall that 1 radian = 57 degrees
   (roughly) so 1 radian = 2x10^5 arcsec (roughly)]

Part III: measure Spitzer Space Telescope image PSF widths and compare w/
expected PSF widths

7) Download the Spitzer Space Telescope images of the V1647
   Ori region from the class website,
   http://www.cis.rit.edu/class/simg217/
   These are MIPS images at wavelengths of 24 and 70 microns.

8) Repeat steps 2-6 above, for the Spitzer images. 

   NOTE: it appears to me that the image of V1647 Ori is
   saturated ("burnt out") in the 24 micron image. (Why do I
   say this?) So you should use a different star in the 24
   micron image field, to measure the PSF FWHM. See if you
   can identify which star you've picked, in the 2MASS
   images -- what is its J-K color? (Or work backwards, pick
   a very 'red' star in J-K and see if it turns up as a
   bright 24 micron source!)

As with the previous assignments, write up your results in
intelligible and logical/sequential fashion (i.e. don't just
submit a pile of numbers). Include graphs and images as
necessary to illustrate how you obtained your results.